In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert-Schmidt kernels are...

In this paper, we study the consistency of the regularized least square regression in a general reproducing kernel Hilbert spaces. We characterized the compactness of the inclusion map from a reproducing kernel Hilbert space to the space of continuous functions and showed that the capacity based analysis by uniform covering numbers may fail in a very general setting. We prove the consistency an...

By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new Fourier transform in general setting processes. Our results serve unify existing tools from analysis.

A framework for coherent pattern extraction and prediction of observables measure-preserving, ergodic dynamical systems with both atomic continuous spectral components is developed. This based on an approximation the generator system by a compact operator Wτ reproducing kernel Hilbert space (RKHS). The skew-adjoint, thus can be represented projection-valued measure, discrete compactness, associ...

A family of regularized least squares regression models in a Reproducing Kernel Hilbert Space is extended by the kernel partial least squares (PLS) regression model. Similar to principal components regression (PCR), PLS is a method based on the projection of input (explanatory) variables to the latent variables (components). However, in contrast to PCR, PLS creates the components by modeling th...